Render and saving image progressively by adding samples
What you ask is not possible directly. It's possible only to use a workaround - basically the same technique as for stacking images in compositor. 

Render with Progressive Refine enabled (to get the whole image at once) until satisfied with amount of noise for one iteration, stop the render. Change the frame to get different noise pattern. Render once more into another file / render layer (i.e. create additional Render Layer, select it and enable Pin icon to render only active one; repeat for all layers). Overlay the results in the compositor.


Setup with saving to Render Layer nodes is shown; the one with images will be the same but opening files instead. Find the most appropriate file format for that operation

Now once  you decide the image is still too noisy, render several times more and overlay them the same as before (so add several more Render Layer nodes and increase value of the Value node).

Note:  this isn't intended to be used instead of the final render (although it can be used as asked - render the same a bit more and overlay on top of already saved image). While this technique can be used to save the final render results in some cases, in most of them it might not be worth time spent on it. Instead it should provide you with 2 things:


an idea of how the scene looks like with given setup without waiting for [some time] only to preview the render;  
rough understanding of how many samples does your image need to stop looking noisy with given circumstances.